Suppose $x[n]$ and $y[n]$ are two nonzero signals(i.e., $x[n] \neq 0$ for at least one value of n and similarly for $y[n]$).Can the convolution between $x[n]$ and $y[n]$ result in an identically zero signal? In other words, is it possible that $\displaystyle\sum_{k = -\infty}^{k = +\infty}x[k]y[n-k] = 0$ for all n.